Binary Search Tree
A binary search tree keeps smaller keys in the left subtree and larger keys in the right subtree, so search follows one branch at a time when the tree is balanced.
Start with this mental model
A binary search tree keeps smaller keys in the left subtree and larger keys in the right subtree, so search follows one branch at a time when the tree is balanced.
How it works, without unnecessary jargon
BST order gives efficient search only when tree height stays small.
A plain BST may become a chain and degrade to O(n). Balanced trees fix that risk.
Read the algorithm as a sequence of decisions
Identify the invariant that must always remain true.
Follow the read/update path through the structure.
After a mutation, restore the invariant before returning.
Read a tiny input by hand and write down the state after every important operation. For Binary Search Tree, the goal is to make the invariant visible rather than to memorize code.
avg O(log n), worst O(n)
Do not quote this complexity mechanically. Ask which operation or input dimension it describes, then derive the cost from the loops, recursion depth, data-structure operations and any preprocessing assumptions.
Good fit
- Choose it when its dominant operations match your workload.
- Compare memory overhead as well as Big-O.
What usually goes wrong
- Memorizing complexity without understanding representation.
- Ignoring worst-case shape or resizing/rebalancing costs.
A professional answer shape
Always qualify O(log n) with 'when balanced'. A plain BST has O(n) worst-case search/insert/delete.
What problem does Binary Search Tree solve?
A binary search tree keeps smaller keys in the left subtree and larger keys in the right subtree, so search follows one branch at a time when the tree is balanced.
What should I mention about complexity?
Its typical cost here is avg O(log n), worst O(n), but a complete answer should connect that cost to the representation, input constraints and the dominant operations.
What is the most common mistake?
Memorizing complexity without understanding representation.